Example 3.9  Let \(R=k[\![x,y,u,v]\!]/(xy-uv)\) , \(M=(x,u)\) , \(N=M^\ast \) , and \(\operatorname{\mathcal {Z}}=\mathfrak {m})\) . It has been established in [1]} that
\(M\)  is a maximal Cohen-Macaulay \(R\) -module which is locally free on the punctured spectrum of \(R\) . Also, one can check that there is an isomorphism \(M\otimes _R N\simeq \mathfrak {m}\) .
